Just wondering if someone could have a quick look over what I've done so far:

Assuming zero initial conditions, solve the following DE:

The Laplace Transform gives:

Rearranging and using the fact that gives us

So ?

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- Oct 12th 2011, 02:19 PMcraigBasic Laplace Transform of a 1st order Differential Equation
Just wondering if someone could have a quick look over what I've done so far:

**Assuming zero initial conditions, solve the following DE:**

The Laplace Transform gives:

Rearranging and using the fact that gives us

So ? - Oct 12th 2011, 03:09 PMJesterRe: Basic Laplace Transform of a 1st order Differential Equation
After taking the Laplace transform, where did the come from?

- Oct 13th 2011, 12:11 AMcraigRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 12:40 AMFernandoRevillaRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 01:30 AMcraigRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 01:38 AMcraigRe: Basic Laplace Transform of a 1st order Differential Equation
So for we have:

So ?

Thanks again for the replies. - Oct 13th 2011, 02:25 AMFernandoRevillaRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 02:43 AMAckbeetRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 03:05 AMFernandoRevillaRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 03:18 AMcraigRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 05:08 AMFernandoRevillaRe: Basic Laplace Transform of a 1st order Differential Equation
- Oct 13th 2011, 05:32 AMAckbeetRe: Basic Laplace Transform of a 1st order Differential Equation
Agreed. You could simply say that you extend the solution found by the LT method to the entire real line. The result of the inverse LT does have the unit step functions in it, and, in fact, does not satisfy the DE for negative t's. However, with the theorem you have invoked, you can extend the solution by eliminating the unit step function.

- Oct 14th 2011, 12:57 AMcraigRe: Basic Laplace Transform of a 1st order Differential Equation
Thankyou both! I don't think we've covered this in lectures yet but I think it makes sense.